Mathematical Biology Seminar
Biological systems such as school of fish rely on multiple mechanisms to perceive the environment and actions of other group members. Such multiple mechanisms enable resilience to environmental uncertainty and non-stationarity. For example, fish may rely on visual perception in calm water and switch to olfactory perception in turbulent water. The social interaction associated with different sensing modalities are different – the visual perception graph describing which fish can see a given fish and the olfactory graph describing which fish can smell the other fish are different. In this talk, I will focus on modeling such interactions using multi-layer networks and discuss information assimilation in these networks. First, I will discuss diffusion of innovation in such networks using a linear threshold model and derive some novel measures of centrality in multi-layer networks. I will then focus on an epidemic propagation model in a multi-layer network in which the network is induced by the mobility of individuals across environmental patches and multiple layers correspond to different mobility patterns. I will discuss the influence of mobility on the stability properties of epidemic equilibria.